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lec 2F.1 Albert R Meyer, February 17, 2012
Mathematics for Computer Science
MIT 6.042J/18.062J
Predicate Logic,III
∀ ∃ in English
Two Meta-Theorems
lec 2F.2 Albert R Meyer, February 17, 2012
Au
Math vs. English
Poet:
G
- Au
“All that glitters is not gold.” ∀x. [G(x)
IMPLIES NOT(
(x))]
No :gold glitters like gold!
lec 2F.3 Albert R Meyer, February 17, 2012
Math vs. English
Poet:
necessarily
- “All that glitters is not gold.”
NOT( x
∀ . [ ( G A x) IMPLIES u(x)])
(Poetic license)
lec 2F.4 Albert R Meyer, February 17, 2012
Math vs. English
Poet: “There is a season to every purpose under heaven”
∃s ∈Season∀p ∈Purpose. s is for p
Some season, say Summer, is good for all Purposes? NO, Summer no good for snow shoveling
lec 2F.5 Albert R Meyer, February 17, 2012
Math vs. English
Poet: “There is a season to every purpose under heaven”
∃s ∈Season∀p ∈Purpose. s is for p
- Poet’s meaning flips the quantiers
lec 2F.6 Albert R Meyer, February 17, 2012
Math vs. English
Poet: “There is a season to every purpose under heaven”
∀p ∈Purpose ∃s ∈Season. s is for p
Poet’s meaning flips the quantiers